Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, k\neq 0$. $\dfrac{{p^{2}}}{{(p^{-4}k^{4})^{-2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{2}}$ to the exponent ${1}$ . Now ${2 \times 1 = 2}$ , so ${p^{2} = p^{2}}$ In the denominator, we can use the distributive property of exponents. ${(p^{-4}k^{4})^{-2} = (p^{-4})^{-2}(k^{4})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{p^{2}}}{{(p^{-4}k^{4})^{-2}}} = \dfrac{{p^{2}}}{{p^{8}k^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{2}}}{{p^{8}k^{-8}}} = \dfrac{{p^{2}}}{{p^{8}}} \cdot \dfrac{{1}}{{k^{-8}}} = p^{{2} - {8}} \cdot k^{- {(-8)}} = p^{-6}k^{8}$.